Seminario Geometría
Homogeneous \(G_2\) and Sasakian instantons on the Stiefel 7-manifold
Ponente: Andrés Moreno (Unicamp, Brasil)Fecha: miércoles 04 de diciembre de 2024 - 11:30Lugar: Aula Naranja, ICMAT
Resumen:
We study the instanton condition for homogeneous connections on the seven dimensional Stiefel manifold \(V^{5,2}=SO(5)/SO(3)\) in the context of \(G_2\) and Sasakian geometry. According to the reductive decomposition of \(V^{5,2}\), we provide an explicit description of all invariant \(G_2\) and Sasakian structures on the Stiefel 7-manifold. In particular, we characterise the invariant G2-structures inducing a Sasakian metric, among which the well known nearly parallel G2-structure (Sasaki-Einstein) is included. As a consequence, we classify the invariant connections on homogeneous principal bundles over \(V^{5,2}\) with gauge group U(1) and SO(3), satisfying either the \(G_2\) or the Sasakian instanton condition. As an application, we analyse the Yang Mills condition for those invariant connections.This is joint work with Luis Portilla (Univ. Brest).
